Numerical Simulation
of Aerosol Transport of spray chambers and aerosol transport can improve the analytical figures of merit in laser ablation ICPMS.
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chain is as as strong as its weakest link. This proverb holds true especially for all analytical methods that consist of different experimental parts. Mistakes or imperfect arrangements give rise to poor analytical performance even when the measuring instrument is perfect. A very important part of chemical analysis is always sample introduction, which, together with sampling and sample preparation, is at the beginning of an analytical “chain”. For example, in inductively coupled plasma spectrometry [(ICPMS or ICP optical emission spectroscopy (OES)] of liquid samples, the analytical figures of merit depend critically on the droplet production by nebulization and the efficiency of the spray chamber. The function of the spray chamber is to condition the aerosol, that is, to separate the useful small droplets from the bigger ones and transport them by a laminar gas flow into the plasma. Inefficient separation results in losses of fine particles and leads to a reduction of the analytical signal, while turbulence in the transport gives rise to noise, thereby reducing the S/N of a measurement (1–3). The same applies for the coupling of ICPMS with laser ablation (LA) of solid samples, in which dry aerosol particles produced by the laser have to be transported into the ICP. However, in this case, the element composition of laser-produced particles is size dependent (4–6), which leads to
in Atomic Spectrometry
Computer simulations
Joachim Koch, Gerhard Schaldach, Harald Berndt, and Kay Niemax Institute of Spectrochemistry and Applied Spectroscopy and University of Muenster (Germany) © 2004 AMERICAN CHEMICAL SOCIETY
A P R I L 1 , 2 0 0 4 / A N A LY T I C A L C H E M I S T R Y
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or operating conditions at pressures or temperatures that deviate from normal.
Numerical computer simulations of spray chambers The first step of a numerical spray chamber simulation is the partitioning of the virtual chamber volume. The so-called numerical grid compartmentalizes the chamber into a large number of small subvolumes or cells (~100,000–1.5 million, depending on the type of spray chamber). The size of the individual Nebulizer tip cells is not uniform but depends on the velocity gradient of the gas flow—the fluid field— in particular parts of the spray chamber volume. The cells have to be small in regions with large velocity gradients, for example, near the nebulizer nozzle, though they can be much larger in other parts of the chamber. In general, the number of cells determines FIGURE 1. Sections of the grid structure of a cyclone spray chamber used the spatial resolution, the accuracy of the simfor numerical simulations. ulation, and the computer processing time needed. A very fine grid may optimize the description of the spray chamber, but it ties up the computer for too long. Therefore, a comthe complicated requirement that all of the aerosol particles promise always has to be made between resolution, quality of approach, and calculation time. Figure 1 shows parts of the grid produced must be introduced into the ICP. In the past, the design and size of spray chambers and LA structure of a cyclone spray chamber used for optimization of cells were developed empirically, with the physical principles of that popular device (9). The total number of cells in this parparticle transport in gases taken into account. The optimization ticular case was ~130,000. Note that the grid sizes are small was performed by the time-consuming and costly principle of near the tip of the concentric nebulizer, the impact area of the trial and error. Therefore, it is not surprising that the commer- tangentially introduced sample nebula, and the center of the outcial spray chambers and LA cells used in atomic spectrometry let. In these parts, the gas velocity and the mass flow have their largest values. do not always achieve top performance. For each cell, the Navier–Stokes equations must be solved. Modern computer programs have the power to simulate the processes in the spray chamber and to describe quantitatively These second-order partial differential equations take into acthe transport of dry aerosols in LA-ICPMS. They can dramat- count the fluid phase (transport gas). Additionally, the aerosol ically shorten the time needed for optimizing particular arrange- droplets (liquid particle phase) are treated as single particles by ments and give the best parameters for the glassblower or the the Lagrangian approach. The main processes to be considered workshop that is building the spray chamber or LA cell. In par- are turbulence of the particle flow, compressibility of the gas, ticular, computational fluid dynamics (CFD) can help to simu- evaporation, droplet–droplet collision, droplet–wall impact, gravilate the sample introduction processes in ICP spectrometry. tational settling, and coalescence of droplets. As input, CFD of spray chambers needs the following inforSuch programs are widely used in different fields of engineering—for example, to optimize instruments such as aerosol par- mation: knowledge of the strongly dispersed primary aerosol distribution produced by the nebulizer nozzle, gas velocity, and ticle samplers (7) or plasma sprayers with aerosol transport (8). In mechanical engineering, most problems require only one- spray angle. Meinhard-type concentric nebulizers were used in phase flow calculations, whereas in chemical and plasma engi- all of the following examples. A Doppler particle analyzer can neering, multiphase flows, such as chemical reactions and heat measure the aerosol size distribution, angle of the spray cone, transfer, have to be considered. Computer simulations of aerosol and velocity of the droplets, whereas the gas velocity is given by particle introductions can determine whether particular types of the geometry of the nozzle, the pressure difference, and the commercial spray chambers or LA cells exhibit the best perform- physical gas properties. The paths of individual aerosol droplets depend strongly on ance possible or whether they can be improved. This approach is also a flexible tool for building customer-tailored devices of any their start position and the properties of the fluid field of the size. For example, the geometry of spray chambers can be opti- gas. In principle, each droplet needs to be considered separatemized for high-throughput conditions, small sample volumes, ly because it has an individual trajectory and interaction in the liquid samples having viscosities different from that of pure water, spray chamber. Unfortunately, this is beyond the scope of an 10 mm
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economical numerical calculation. To obtain representative results, a very high number of trajectories of droplets with typical diameters have to be calculated. Usually the simulation of ~20,000–30,000 individual trajectories is sufficient to obtain reasonably good results. These trajectories should represent roughly 108 droplets/s in about 25 different size classes (1–25 µm diam). Even a powerful computer, such as the IBM SP2, would take >10 h to complete the job. The first step in total simulation of a particular chamber design requires the solution of the fluid field equations without particles. Subsequently, the aerosol particles are taken into account as described earlier. The interaction of the droplets with the gas (exchange of momentum and energy) affects the fluid field, so the modified fluid field has to be calculated. Next, the interaction between the droplets and the modified fluid field is evaluated, which leads to a further improved fluid field. That field, in turn, is the input of the next iteration. Results typically converge after 5–10 iterations. Again, droplet coalescence, gravitation, and orientation of the spray chamber in space have to be included in the model in order to obtain realistic data (9–12). The results of the CFD procedure can be displayed as 2-D and 3-D graphical presentations of the gas and aerosol flow inside the spray chamber at any angle of observation and with a desired spatial resolution at different times of evolution. For example, Figure 2a uses different colors to show the gas velocity distribution in the central plane of a vertical cyclone spray chamber (8). At the nebulizer tip, the gas speed is near the velocity of sound (>200 m/s). Because of the adiabatic expansion into a relatively large volume, this value drops to ~20 m/s at ~2 mm (hot pink) from the nebulizer tip (9). The gas stream is deflected at a large angle from the chamber wall and leads to a rotating gas flow (red, which indicates 2 m/s), which is then redirected by the spoiler at the bottom (orangeyellow, which indicates 1.4 m/s). The flow at the outlet is
